Why it matters

Randomization gives guarantees deterministic can't. Understanding shapes algorithm design.

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The architecture

Las Vegas: correct output, randomized runtime.

Monte Carlo: correct with high probability.

Randomized algo examplesRandom pivotQuicksort avgRandom hashuniform distRandom prime testMiller-RabinPRNG quality matters; adversaries exploit weak randomness
Randomization uses.
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How it works end to end

Expected complexity: probability-weighted worst case.

Amortized: analyze across operations.

PRNG choice: crypto vs statistical uses.